AP Physics B. Closed / Both Ends
L = distance between walls String fixed at both ends L = (nl/2) n = 1,2,3 .... since v=fl then f_{n} = n[v/2L]
n = 1,2,3 .... Each frequency is a multiple of the fundamental frequency
C. Closed at One End L= [n/4]l n = 1,3,5,7 ..... since v=fl then f_{n} = nv/4L n = 1,3,5,7 ..... frequency goes up by 2 times fundamental and are divisible by ODD number
D. Open at Both Ends Giancoli p. 348) 34, 36
34) Closed 88 Hz is fundamental 36) Open Pipe Fundamental 40 Hz, both are even number multiples of 40 not odd multiple of 20
f = v/2L = 40 Hz = (340 m/s)/2L L = 4.3 m
Review Book p. 302) 10.
Open at one end n = 1 fundamental f = v/4L = 340 m/s/(4 x .17) = 500 Hz
p. 303) 10
Beats  Rhythmic interference between two semi identical frequency sources
Beat Frequency = f_{1}  f_{2}
Enrichment
Standing Waves  Wake Forest .U.
Large_Free_Sphere_of_Water.mov
)
ŠTony Mangiacapre.,
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